Finite Group Databasebeta

← C13×#11575 #15697914

Subgroups — C13×#11575 #15697914

Order 3328.

554 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2409C211yesmaximal, characteristic
2C13×#1466C211yesmaximal, characteristic
3C13×#1459C211yesmaximal, characteristic
4C13×#1326C214yesmaximal, complemented
5C23×Q8×C13C411yescharacteristic
6C2×C13×C22⋊Q8—21no—
7C2×C4×D4×C13C2211yescharacteristic
8C13×#432—21no—
9C2×C13×C22⋊C8—21no—
10C13×#395—21no—
11C13×#393—21no—
12C13×#391—21no—
13C13×#386C412yes—
14C13×#385C2212yes—
15C13×#380C411yescharacteristic
16C13×#324—21no—
17C13×#323—21no—
18C13×#323C2212yes—
19C13×#323C2212yes—
20C22×Q8×C13—21no—
21C22×Q8×C13—21no—
22C22×Q8×C13—41no—
23C22×Q8×C13—41no—
24C22×Q8×C13—44no—
25C22×D4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13C2×C412yes—
28C23×C4×C13D411yescharacteristic
29C22×C8×C13—41no—
30C13×C22⋊Q8—44no—
31C4×D4×C13—41no—
32C4×D4×C13—41no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4C2×C412yes—
38C2×C13×C22⋊C4D411yescharacteristic
39C2×C13×C22⋊C4C2311yescharacteristic
40C2×C42×C13D411yescharacteristic
41C13×C4⋊C8—41no—
42C13×C22⋊C8—22no—
43C13×C22⋊C8—22no—
44C13×C22⋊C8—41no—
45C13×#97—41no—
46C13×#95—21no—
47C13×#95—22no—
48C13×#95—22no—
49#11575C1311yesmaximal, characteristic, direct product factor, Sylow
50C24×C13C22⋊C411yescharacteristic
51C24×C13C22×C411yescharacteristic
52C2×Q8×C13—24no—
53C2×Q8×C13—42no—
54C2×Q8×C13—44no—
55C2×Q8×C13—42no—
56C2×Q8×C13—44no—
57C2×Q8×C13—48no—
58C2×Q8×C13—44no—
59C2×Q8×C13—41no—
60C2×Q8×C13—41no—
61C2×D4×C13—22no—
62C2×D4×C13—22no—
63C2×D4×C13—41no—
64C22×C4×C13—22no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—22no—
70C22×C4×C13—42no—
71C22×C4×C13—44no—
72C22×C4×C13—42no—
73C22×C4×C13—42no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C2×C8×C13—42no—
80C2×C8×C13—42no—
81C2×C8×C13—82no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—42no—
84C13×C4⋊C4—44no—
85C13×C22⋊C4—24no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—44no—
89C42×C13—21no—
90C42×C13—21no—
91#2409C2×C1311yescharacteristic
92#1466C2×C1311yescharacteristic
93#1459C2×C1311yescharacteristic
94#1326C2×C1314yescomplemented
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13#10112yes—
104C23×C13C2×C22⋊C411yescharacteristic
105C23×C13#13112yes—
106Q8×C13—44no—
107Q8×C13—48no—
108Q8×C13—44no—
109D4×C13—44no—
110C2×C4×C13—22no—
111C2×C4×C13—24no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—44no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—44no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—81no—
132C2×C4×C13#9911yescharacteristic
133C2×C4×C13#9911yescharacteristic
134C8×C13—82no—
135C8×C13—82no—
136C23×Q8C4×C1311yescharacteristic
137C2×C22⋊Q8—21no—
138C2×C4×D4C22×C1311yescharacteristic
139#432—21no—
140C2×C22⋊C8—21no—
141#395—21no—
142#393—21no—
143#391—21no—
144#386C4×C1312yes—
145#385C22×C1312yes—
146#380C4×C1311yescharacteristic
147#324—21no—
148#323—21no—
149#323C22×C1312yes—
150#323C22×C1312yes—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—22no—
154C22×C13—22no—
155C22×C13—42no—
156C22×C13—42no—
157C22×C13—42no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—81no—
163C22×C13#40811yescharacteristic
164C22×C13C2×#9911yescharacteristic
165C22×C13C2×#10111yescharacteristic
166C4×C13—21no—
167C4×C13—41no—
168C4×C13—44no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—82no—
173C4×C13AΣL(1,𝔽16)12yes—
174C22×Q8—21no—
175C22×Q8—21no—
176C22×Q8—41no—
177C22×Q8—41no—
178C22×Q8—44no—
179C22×D4C2×C4×C1311yescharacteristic
180C23×C4C2×C4×C1311yescharacteristic
181C23×C4C2×C4×C1312yes—
182C23×C4D4×C1311yescharacteristic
183C22×C8—41no—
184C22⋊Q8—44no—
185C4×D4—41no—
186C4×D4—41no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4D4×C1311yescharacteristic
190C2×C22⋊C4—22no—
191C2×C22⋊C4C2×C4×C1312yes—
192C2×C22⋊C4D4×C1311yescharacteristic
193C2×C22⋊C4C23×C1311yescharacteristic
194C2×C42D4×C1311yescharacteristic
195C4⋊C8—41no—
196C22⋊C8—22no—
197C22⋊C8—22no—
198C22⋊C8—41no—
199#97—41no—
200#95—21no—
201#95—22no—
202#95—22no—
203C2×C13—21no—
204C2×C13—21no—
205C2×C13—42no—
206C2×C13—42no—
207C2×C13#147211yescharacteristic
208C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
209C2×C13#212311yescharacteristic
210C24C13×C22⋊C411yescharacteristic
211C24C22×C4×C1311yescharacteristic
212C2×Q8—24no—
213C2×Q8—42no—
214C2×Q8—44no—
215C2×Q8—42no—
216C2×Q8—44no—
217C2×Q8—48no—
218C2×Q8—44no—
219C2×Q8—41no—
220C2×Q8—41no—
221C2×D4—22no—
222C2×D4—22no—
223C2×D4—41no—
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—42no—
231C22×C4—44no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4C13×C22⋊C411yescharacteristic
235C22×C4C13×C22⋊C411yescharacteristic
236C22×C4C13×C22⋊C411yescharacteristic
237C22×C4C2×D4×C1311yescharacteristic
238C22×C4C2×D4×C1311yescharacteristic
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—82no—
242C4⋊C4—41no—
243C4⋊C4—42no—
244C4⋊C4—44no—
245C22⋊C4—24no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—44no—
249C42—21no—
250C42—21no—
251C13#1157511yescharacteristic, direct product factor, Sylow
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23C13×#10112yes—
261C23C2×C13×C22⋊C411yescharacteristic
262C23C13×#13112yes—
263Q8—44no—
264Q8—48no—
265Q8—44no—
266D4—44no—
267C2×C4—22no—
268C2×C4—24no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—44no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—44no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—81no—
289C2×C4C13×#9911yescharacteristic
290C2×C4C13×#9911yescharacteristic
291C8—82no—
292C8—82no—
293C22—21no—
294C22—21no—
295C22—22no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—41no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—81no—
305C22C13×#40811yescharacteristic
306C22C2×C13×#9911yescharacteristic
307C22C2×C13×#10111yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—44no—
312C4—41no—
313C4—41no—
314C4—82no—
315C4C13×AΣL(1,𝔽16)12yes—
316C2—21no—
317C2—21no—
318C2—42no—
319C2—42no—
320C2C13×#147211yescharacteristic
321C2C2×C13×AΣL(1,𝔽16)11yescharacteristic
322C2C13×#212311yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC22×D4×C13C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C13×#1326C2semidirect
49. #11575C13direct (N × H)
94. #1326C2×C13semidirect
251. C13#11575direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C13×#24092
C13×#14662
C13×#14592
C13×#13262
#1157513